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Random rotation

As explained in Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI

A random rotation is a reversible transformation that applies a randomly selected orthogonal rotation to input feature vectors.

Random rotation applies a randomly selected rotation matrix to input feature vectors before modeling. Because the square orthogonal matrix preserves vector lengths and angles, the transformation is reversible and keeps the data geometrically equivalent. section 5.2.3

Comparing tabular models

Rotate a tabular dataset, then compare gradient-boosted decision trees with a deep neural network. Deep architectures may outperform after rotation because they can learn rotated signals, while tree models rely on axis-oriented splitting rules. Treat this result as evidence of a limitation in the tree model, not automatic proof that deep learning is superior. section 5.2.3

Use random rotation when you need to:

  • Test model sensitivity to feature orientation. section 5.2.3
  • Improve ensemble diversity or robustness. section 5.2.3
  • Address rotation-invariance requirements in computer vision or quantum chemistry. section 5.2.3

How Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI covers it

How deep it goes
Defines the matrix properties and explains model trade-offs, but does not provide implementation steps or derivations.
Examples
Uses rotated tabular data to contrast gradient-boosted trees with deep neural networks.
What it assumes
Assumes feature vectors and basic model categories, while defining orthogonal rotation properties from zero.
What you can do after
Apply a reversible rotation before modeling to test orientation sensitivity and compare tree-based with deep-learning approaches.
How it connects
Connects random rotation with gradient boosting, deep learning, ensemble methods, rotation invariance, computer vision, and quantum chemistry.
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Related concepts

This explainer was generated by Manning's knowledge graph from the text of Machine Learning for Tabular Data: XGBoost, Deep Learning, and AI. The section links point to the parts of the book it draws on.